The chkconfig "on" and "off" commands update symlinks in runlevel-specifc subdirectories that init uses.
There is "chkconfig --add tomcat8" command to create the initial symlinks.
The chkconfig requires that the script file "/etc/init.d/tomcat8" contains configuration instructions as comments in format that chkconfig uses. Furthermore, the script should accept at least command line parameters "start" and "stop".
It is quite possible that a non-RPM-packaged program does not have a startup script that chkconfig can use. One could create such separate script for chkconfig that merely calls the actual startup script as appropriate.
However, it is not yet clear what the "RH Enterprise" is. There is RedHat Enterprise Linux (RHEL), but it has several major releases the latest being RHEL 7.
Up to RHEL 6 the service management did use chkconfig. RHEL 7 has replaced that with systemd and only a couple old services remain with only the chkconfig-style configuration and the chkconfig-command is a mere wrapper for systemctl. The systemd service configuration is entirely different.
There are a lot of strong opinions about systemd, even though several distros have adopted it recently.
Websearch suggests:
http://tomcat.apache.org/tomcat-8.0-doc/setup.html#Unix_daemon
In other words, the contents of $CATALINA_HOME/bin/daemon.sh are interesting.